The water is generally used as a finishing fluid of the conventional electrode discharge machine in view of the fact that the finishing chore of a work piece of a steel material can be done rapidly, safely and economically. In addition, the finishing fluid of water is not detrimental to the environment. However, the use of water as the finishing fluid of the conventional electrode discharge machine is not suitable for drilling the fine holes in a work piece made of an altiminium or tungsten steel material because of the facts that the quality of water plays an important role in then stability of the conductivity of the fine holes, and that the fine holes can not be drilled with precision, and further that the water conductivity is so undermined as to prolong the drilling process. When the drilling process is done on a workpiece of an aluminum material, the water and the aluminiumn can be caused by the electric discharge to form the aluminiumn oxide on the surface of the workpiece, thereby resulting in the poor conductivity of the workpiece. The above shortcomings can be easily overcome by using the electrode discharge machine oil in place of water. However, the conventional electrode discharge machine is not provided with a fluid circulating system capable of dual functions of circulating water or oil interchangeably. It must be pointed out here that the use of oil as a finishing fluid of the electrode discharge machine can result in an increase in the cost of the drilling process as well as the risk of the environmental pollution.